Specializing in Problems That Only Seem Impossible to Solve

“It’s a little plastic toy,” said Jessica Fridrich, tossing a Rubik’s Cube between her long-fingered hands on a stormy afternoon in her office at Binghamton University, her fingernails painted with a pastel pink gloss.

But the little toy, an icon of the era of Pac-Man and high-top sneakers, has made a big comeback. For a thriving subculture of people who try to solve the cube as fast as possible, Dr. Fridrich is a pioneer and a patron saint. She forged what remains arguably the world’s most common strategy for speed-solving the puzzle, and appeared in a documentary about the Rubik’s Cube released this fall.

Dr. Fridrich first cracked the colorful walls of the Rubik’s Cube in 1981 as a teenager living in a Czech coal mining city. Few people will spend decades decoding a plastic block, no matter how mathematically intricate. But few people are as tenacious as the architect of “The Fridrich Method,” a roadmap that requires a speedcuber to memorize and unleash at least 53 algorithms, each of which is a series of turns of the cube’s rows and columns in a given sequence.

For Dr. Fridrich, tackling an impossible puzzle is not a hobby, and the Rubik’s Cube is not simply a game. They are obsessions.

Trapped in Czechoslovakia until the Velvet Revolution made migration to the United States for doctoral study possible, Dr. Fridrich, self-taught in differential and integral calculus, sketched out a solution to the Rubik’s Cube in a tattered notebook even before owning one.

Dr. Fridrich, 44, an electrical engineering professor, is frequently confronted at academic conferences and asked to solve the cube on the spot. She fields e-mail messages from 13-year-olds in Japan and has inspired scores of YouTube videos from cube enthusiasts riffing on her method, which was propagated on the Internet in the late 1990s as the puzzle saw a resurgence.

“She chose the basic route, the direction we would take up the mountain,” said Dan Knights, winner of the 2003 World Rubik’s Cube Championship (Dr. Fridrich placed second). “And other people are finding different ways from one ledge to another.”

Mr. Knights, 29, used the Fridrich Method to win the 2003 competition after seeking her out as a mentor four years earlier. At first confounded by her techniques, he took a year off from college to learn them while traveling by train through Europe and Asia.

The Fridrich Method requires first solving the top two layers of the three-tiered Rubik’s Cube, selecting the face with the central white square as the roof. (Each face has a middle square of a distinct color attached to the cube’s central joint that dictates the color the face will be when solved.) Most speedcubers learn to do this by intuition, improvising until the white face remains intact and other squares fall into place on their correctly colored sides. The crux of the Fridrich Method lies in solving the third and last layer of the cube without compromising the color scheme put into place in the initial steps.

To solve the third layer, the speedcuber must assemble all of the yellow squares on the bottom face by applying one of 40 algorithms in a phase called “orientation.” The cuber must instantly recognize which algorithm to apply in order to have any hope of solving it with haste. In the final step, permutation, one of 13 algorithms restores the cube’s chromatic harmony, one color per face.

The world’s fastest speedcubers, including Dr. Fridrich, know more than 100 algorithms to whisk the cube to its solution. They recognize when the puzzle is jumbled or positioned in their palms in a way that one set of moves is quicker than 99 others.

As a teenager, Dr. Fridrich saw a man demonstrating the Rubik’s Cube at a mathematics seminar, and scrambled defiantly through a crowd to touch it. She says it was immediately clear that she was “cube possessed,” her shorthand for people who spend most of their waking hours learning to speed-solve the cube. Even though no cubes were for sale in her country then — the few people who had them bought them in Hungary — she would not be stopped. She picked up Kvant, a Russian math journal that outlined one method of solving the cube, and worked it out on paper.

When she finally got her first cube, left behind by family friends visiting from France, she began to improvise, cubing faster and faster to beat record times from Prague, Hungary and the United States printed in newspapers. By the time the Czech national championship took place in 1982, Dr. Fridrich was one of the fastest speedcubers in the country. She won the championship, solving the cube in less than 23 and a half seconds — a time that would now be laughably long in international competition — going onto place 10th in the first world championship in Budapest.

An error has occurred. Please try again later.

You are already subscribed to this email.

After earning her master’s degree, she was building mathematical models of rock deformation at a mining institute when she was recruited by a professor from Binghamton who heard about her mastery of the cube and her grades at the Czech Technical University in Prague. After a brief meeting in which she described her cube algorithms, he asked her to apply for the doctoral program in systems sciences. She had no résumé, so she dashed one off on a typewriter just before the professor’s train left the station. A year later, she arrived in Binghamton, where she has lived ever since.

In her research in digital forensics, Dr. Fridrich uses computers to tackle another seemingly intractable puzzle: matching a photograph with the individual camera that took it. Law enforcement agencies plan to use the techniques to track down child pornographers and movie pirates.

“She looks at a problem that seems insolvable,” said George J. Klir, the retired professor who recruited her 18 years ago. “And she finds a way to solve it, again and again.”

Dr. Fridrich was drawn to “camera ballistics” because of its inscrutable mysteries, similar to those the Rubik’s Cube held in the early ’80s. “It was very visual,” she said. “Usually when you develop an algorithm or a formula you cannot really see it.”

When Dr. Fridrich forged her Rubik’s Cube algorithms, she did so by trial and error, using only pencil, paper and a cube. Today, the cube is no longer an uncharted territory like digital forensics, but a terrain well-plowed by personal computers and the sweaty palms of speedcubers.

Software programs can compute the quickest solution to any given mix-up of the cube’s faces. Hundreds, possibly thousands of speedcubers have tweaked the Fridrich Method to work with a technique called “finger pushing,” best used on cubes with joints eased loose by repetitive stress so you can flick their walls instead of grabbing rows to rotate them. Now, Dr. Fridrich said, the cube has been “optimized to death,” and holds little allure — even though she still keeps nearly 20 of the plastic puzzles scattered around her office and home.

Dexterity once defined Dr. Fridrich, who now uses just six fingers to hunt and peck on her keyboard. She has been far surpassed by speedcubers with records of 14, 13 and 10 seconds, some of whom can solve the cube blindfolded after studying it for less than a minute. “Today I would probably be in 20th or 30th place,” she said. “I am letting it go because I think it’s time for others to succeed.”

For someone who wins for the sake of winning, who never roots for the underdog, in sports or in life, this retreat from speedcubing seems something like a reluctant acceptance that some things are indeed, impossible.

At the very least, she admitted, “it’s not yet possible to do everything at once.”

A version of this article appears in print on , on Page D3 of the National edition with the headline: Specializing in Problems That Only Seem Impossible to Solve. Order Reprints|Today's Paper|Subscribe